Dario Trevisan Università degli Studi di Pisa Dipartimento di Matematica Largo Bruno Pontecorvo, 5 Pisa, 56127, Italy Mobile: +39 331 2899761 Email: dario.trevisan@unipi.it Homepage: http://people.dm.unipi.it/trevisan/ Areas of specialization Mathematical probability and analysis: ordinary, stochastic and partial differential equations; Markov processes and semigroups; Gaussian analysis (Malliavin calculus); functional inequalities. Current position (Since 2015) Assistant professor at Università degli Studi di Pisa, Italy Education 2011-2014 Perfezionamento (Ph.D.) in Mathematics, Scuola Normale Superiore 2006-2011 Diploma corso ordinario, Scuola Normale Superiore 2009-2011 Laurea magistrale (M.Sc.) in Mathematics, Università degli Studi di Pisa 2006-2009 Laurea triennale (B.Sc.) in Mathematics, Università degli Studi di Pisa Publications Since 2012, I have been (co-)author of 18 articles published in international scientific journals and 1 contribution in peer-reviewed volumes (n. 14). 2018 1. V. Magnani, E. Stepanov, D. Trevisan, A rough calculus approach to level sets in the Heisenberg group, 2. L. Ambrosio, F. Stra, D. Trevisan, A PDE approach to a 2-dimensional matching problem, Probability Theory and Related Fields, (online first) DOI: 10.1007/s00440-018-0837-x 3. G. de Palma, D. Trevisan, The Conditional Entropy Power Inequality for Bosonic Quantum Systems Communications in Mathematical Physics, Communications in Mathematical Physics (online first) DOI: 10.1007/s00220-017- 3082-8 2017 4. G. de Palma, D. Trevisan, V. Giovannetti, Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels, Physical Review Letters, vol. 118, n. 16, DOI: 10.1103/physrevlett.118.160503
Dario Trevisan 2 5. L. Ambrosio, D. Trevisan, Lecture notes on the DiPerna-Lions theory in abstract measure spaces, Ann. Fac. Sci. Toulouse, vol. XXVI, p. 729-766, DOI: 10.5802/afst.1551 6. V. Magnani, D. Trevisan, On Lipschitz vector fields and the Cauchy problem in homogeneous groups, Communications in Contemporary Mathematics, (online first), DOI: 10.1142/S0219199717500572 2016 7. E. Musta, M. Pratelli, D. Trevisan, Functional Cramér Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes, Journal of Multivariate Analysis, vol. 154, pp. 135 146, DOI: 10.1016/j.jmva.2016.10.011 8. E. Stepanov, D. Trevisan, Three superposition principles: currents, continuity equations and curves of measures, Journal of Functional Analysis, vol. 272, n.3, DOI: 10.1016/j.jfa.2016.10.025 9. G. De Palma, D. Trevisan, V. Giovannetti, Gaussian states minimize the output entropy of the one-mode quantum attenuator, IEEE Transactions on Information Theory, vol. 63, n. 1, pp. 728 737, DOI: 10.1109/TIT.2016.2621748 10. L. Ambrosio, F. Stra, D. Trevisan, Weak and strong convergence of derivations and stability of flows with respect to MGH convergence, Journal of Functional Analysis, vol. 272, n. 3, DOI: 10.1016/j.jfa.2016.10.030 11. G. De Palma, D. Trevisan, V. Giovannetti, Passive states optimize the output of bosonic Gaussian quantum channels, IEEE Transactions on Information Theory, vol. 62, n. 5, pp. 2895 2906, DOI: 10.1109/TIT.2016.2547426 12. D. Trevisan, Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients, Electronic Journal of Probability, vol. 21, DOI: 10.1214/16-EJP4453 2015 13. D. Trevisan, Lagrangian flows driven by BV fields in Wiener spaces, in Probability Theory and Related Fields, vol. 163, n. 1 (2015), DOI: 10.1007/s00440-014-0589-1 2014 14. D. Trevisan, A short proof of Stein s universal multiplier theorem, in Séminaire de Probabilités XLVI 15. L. Ambrosio and D. Trevisan, Well posedness of Lagrangian flows and continuity equations in metric measure spaces, in Analysis & PDE, vol. 7, n. 5, DOI: 10.2140/apde.2014.7.1179 16. G.M. Dall Ara and D. Trevisan, Uncertainty Inequalities on Groups and Homogeneous Spaces via Isoperimetric Inequalities, in The Journal of Geometric Analysis, DOI: 10.1007/s12220-014-9512-3
Dario Trevisan 3 2013 17. D. Trevisan, BV -regularity for the Malliavin derivative of the maximum of the Wiener process in Electronic Communications in Probability, vol. 18, DOI: 10.1214/ECP.v18-2314 18. D. Trevisan, Zero noise limits using local times, in Electronic Communications in Probability, vol. 18, DOI: 10.1214/ECP.v18-2587 2012 19. M. Pratelli and D. Trevisan, Functions of bounded variation on the classical Wiener space and an extended Ocone-Karatzas formula, in Stochastic Processes and their Applications, vol. 122, DOI: 10.1016/j.spa.2012.03.010 Academic Talks and Posters 2018 1. A PDE approach to random matching problems. Invited talk at Workshop Metrics and Measures, Sendai, 10/01/2018 2017 2. On the parametrization of level sets in the Heisenberg group. Invited talk at workshop Rough paths in Toulouse, Toulouse, 20/10/2017 3. On level sets in the Heisenberg group. Invited talk at Workshop on Geometric Measure Theory, Warwick, 11/07/2017 4. A PDE approach to the 2-dimensional random matching problem. Contributed talk at First Italian meeting in Probability and Mathematical Statistics, Torino, 21/06/2017 5. A rough(-young) calculus approach to level sets in the Heisenberg group. Contributed talk at Seventh Berlin-Oxford meeting, Berlin, 19/05/2017 6. A rough calculus approach to level sets in the Heisenberg group. Contributed talk at XXVII Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 08/02/2017 7. A PDE approach to the 2-dimensional random matching problem. Invited talk at TU Wien, 26/01/2017 2015 8. A particle systems approach to cell-cell interaction. Poster session at CIRM Scientific Event Present Challenges of Mathematics in Oncology and Biology of Cancer, Marseille, 9/12/2015 9. Well-posedness of Multidimensional Diffusion Processes with Weakly Differentiable Coefficients. Invited talk at Oberseminars Stochastics, Bonn, 29/10/2015
Dario Trevisan 4 2014 10. Uncertainty Principle via Isoperimetric Inequalities. Contributed talk at XXXIV Convegno Nazionale di Analisi Armonica, Pisa, 11/06/2014 11. Lagrangian Flows and Continuity Equations on Metric Measure Spaces. Invited talk at Analysis Seminar at Mathematisches Institut, Universität Basel, 26/03/2014 12. Towards a Di Perna-Lions Theory on RCD Spaces. Contributed talk at XXIV Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 30/01/2014 2013 13. A Di Perna-Lions Theory on Wiener Spaces. Invited talk at Seminari di calcolo delle variazioni e analisi geometrica, Università di Pisa, 04/12/2013 14. Diseguaglianza isoperimetrica con tecniche di semigruppi (Isoperimetric Inequalities via Semigroups). Invited talk at Seminari del Dottorato di Ricerca, Università di Firenze, 18/03/2013 2012 15. BV Functions on the Classical Wiener Space: an Extended Clark- Ocone-Karatzas Formula. Contributed talk at PRIN 2008 final conference, Pescara 10/08/2012 16. Malliavin Regularity for sup 0 t T W t. Poster session at Workshop on Stochastic Analysis and Applications, EPFL Lausanne, 06/06/2012 2011 17. BV Functions on the Classical Wiener Space and an Extension of the Clark-Ocone-Karatzas Formula. Contributed talk at 5th ICSAA, Bonn, 05/09/2011 Scientific Projects and Memberships 2017 1. Coordinator (P.I.) of GNAMPA research project Campi vettoriali, superfici e perimetri in geometrie singolari, 03/2017-03/2018 2016 2. Participant in Project PRA 2016 41, Singular Phenomena and Singular Geometries, Università degli studi di Pisa (P.I. prof. M. Romito), 2016 2014 3. Personal research project on Well-posedness of deterministic and stochastic evolution equation, Scuola Normale Superiore (supervisor: prof. L. Ambrosio), 11-12/2014 2013 4. Participant in local group (Pisa, supervisor: prof. L. Ambrosio) PRIN 2010-2011 Calcolo delle Variazioni, P.I. Prof. L. Dal Maso, 01/2013-2014 2012 5. Member of the GNAMPA group Analisi Reale, Teoria della Misura e Probabilità, 2012-ongoing
Dario Trevisan 5 2011 6. Participant in local group (Pisa, supervisor: prof. M. Pratelli) PRIN 2008 Teoria generale dei Processi Stocastici e Finanza Matematica, P.I. Prof. M. Frittelli, 11/2011-2012 Organization of scientific events 2018 1. Organizing committee of mini-workshop Vector Fields, Surfaces and Perimeters in Singular Geometries, Università degli studi di Ferrara, Ferrara 27-28/02/2018 2017 2. Organizing committee of probability summer school Mathematical Modeling in Life Sciences, Centro di Ricerca Matematica Ennio de Giorgi, Pisa 13-16/09/2017 2016 3. Organizing committee of workshop Singular Phenomena and Singular Geometries Università degli studi di Pisa, Pisa 20-23/06/2016 Teaching Activities 2018 Equazioni differenziali stocastiche e applicazioni, at Università degli studi di Pisa (Mathematics), main lecturer, hours: 42 (ongoing) 2017 Calcolo delle Probabilità e statistica, at Università degli studi di Pisa (Informatics), main lecturer, hours: 48 Probabilità superiore, at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Romito, hours: 20 Elementi di Probabilità e statistica at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Pratelli, hours: 4 2016 Calcolo delle Probabilità e statistica, at Università degli studi di Pisa (Informatics), main lecturer, hours: 46 Stochastic Processes and Stochastic Calculus with application to Economics and Finance, Summer School of Mathematics for Economic and Social Sciences, Scuola Superiore Sant Anna, Pisa, (Finance and Economy) 12-16/09/2016, main lecturer prof. M. Pratelli, hours: 8 Istituzioni di Matematica I, at Università degli studi di Pisa (Chemistry), main lecturer prof. E. Fortuna, hours: 50
Dario Trevisan 6 Ricerca operativa II e statistica II, at Università degli studi di Pisa (Engineering), main lecturer prof. F. Flandoli, short introduction to R, hours: 2 Istituzioni di Probabilità, at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Romito, hours: 3 2015 Calcolo delle Probabilità e statistica, at Università degli studi di Pisa (Informatics), main lecturer prof R. Giuliano, hours: 18 Statistica Matematica, at Università degli studi di Pisa (Mathematics), main lecturer prof. R. Giuliano, brief introduction to R, hours: 2 Istituzioni di Probabilità, at Università degli studi di Pisa (Mathematics), main lecturer prof. M. Romito, hours: 20 Elementi di Probabilità e statistica at Università degli studi di Pisa (Mathematics), main lecturer prof. F. Flandoli, hours: 28 2014 TA (tutoring) Complementi di Matematica at Scuola Normale Superiore. Lectures by prof. L. Ambrosio 2013 TA (tutoring) Complementi di Matematica at Scuola Normale Superiore. Lectures by prof. F. Ricci 2012 TA (tutoring) Istituzioni di Probabilità at Università di Pisa. Lectures by F. Flandoli TA (tutoring) Complementi di Matematica at Scuola Normale Superiore. Lectures by by F. Ricci. 2011 Teaching assistant (tutoring): Introduzione alla Teoria della Misura e l Analisi Funzionale at Scuola Normale Superiore. Lectures by L. Ambrosio. Pre-undergraduate Talks 2013 Il problema di Didone, at Corso di orientamento universitario della Scuola Normale Superiore (pre-undergraduate courses), in Rome 2012 L equilibrio di Nash nella teoria dei giochi at Corso di orientamento universitario della Scuola Normale Superiore (pre-undergraduate courses), in San Miniato (Pisa) 2011 Betti, Dini, Bianchi e l insegnamento della matematica guided tours to Scuola Normale Superiore historical math collection (main organizer: A. Andrei)
Dario Trevisan 7 2010 Two lectures on elementary number theory at Settimana Matematica 2010 (pre-undergraduate courses), in Pisa Last updated: March 13, 2018